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.- 第22卷第2期中国科学技术大学学报VOI22,No2 rJON^t.oIN^vEsRlosE^EcHNOLoY.eTGFF 2年6月皿cH1训竹CI胡湘JU1992n99 ConvergeneeRatesofSomeEstimatorsfor 许 aSemiParametrieRegressionModel GaoJiti e ()伸rtmntofMatbematiCS) Abst班Ct · `二`,,,- considertheergonmodel犷“心声+夕()+氏for`一l2…,eHer夕15anun eslr,,`. known加netinninIR二(一coco)e15anuno眺erveddlsutrbance刀晚sedonthekernel anneanerrs,eoeonvereesae desrtihg加estimaot吐,(:)sompt加atsenaret咖t出es往m-a .· torsof刀andg()areobatined 二,一, 众ywordssemi琳rametrieregre绍fonmodelleastsquareest加ateoPtimalconvegtenee rate AMS翻bjeetClas企让.tion(1991):62G07,62J10 1IntrodutCion Consi血rthemodelgivenby ,二 梦`一人刀+g(x`)+伙,落一12…,(1) ,...,, wheer(人:`,e`)are11drandomsamPles(人二`)ande`areindeepndentand氏15hterandomerror ,. wihtmean0andvarianceaZ刀15anunkhownParam亡etrand夕15anunknownfunetion oSmeasympto桩etheoryfor钟riteal印lineest加atosrof刀hasboende穴10讲dbyeHekman[i〕and .,` Riee[幻hTeyinvestisat“htecasewheert5aremodeledas , 人一h(劣`)+价云=1,2,…,(2) whereh15akno、vnfunetionoftheevoariate劣andthe了`忱havelikeezromaen,uneorrelatedrandom . variables . ReceiVedAPr亚30,1991 . 辞ThisPro扭tsuPPort目byNNSFCun血rtheconrraet18901001 130中国朴学扶术大学学报第22卷 ,e,e R侧毖ntlysepckman[,]has血vl叩司anatetrnauvesetimaotrof声in(i)hattunderamodl - suhCas(2)wiht夕andhbohtsmooth,is创沼uredof加vinga琳armetrieconver罗ncearetforistsatn · 血dterrorandasymtPiotaCllynegl语ibleb边5withouttheneceSiytofundersmohting ia., hTeasymtP成eanalyseofeHkCman[]anduE恤nketl[月〕aereon份rn司wi小几=0or价一0 ,,·. `=l2…,wihehaer比战刁on9esitmatedbySPlinesmotbj的9esitmateS :,:`,, InhtePr姗nt劝团ywedlscussthefollowingextremeca,namelythecasewhere=0`=l ,,,二. 2….andh()=公(iwhtoutl端Ofgenerailyt)Thereforewe创铭umethatthe豹followthernodel (the邢”eificcaseof(1)) ,,, 夕`~脚`+夕(x`)+氏云~12,…,(3) .魂, 侃enforinetrestinamodelofhtisform咖msform脉workby血bank以以[〕也eother . rnistaesor汕tthissepeifiemodel15themixedergr创沼ionm团elprop汉姆dbyStone[s〕 easo, 一 E匕翻川onhtelea`tqSuaerest血nator几Of刀andthekernelandneaesrtniehgborestimates么of夕 · someOPt加alartesofeonvergeneeabout几and纵aer由atined 2M.inResultS